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In this study, we investigate the existence of infinitely many radial sign-changing solutions with nodal properties for a class of Kirchhoff-type equations possessing non-odd nonlinearity. By combining variational methods and analysis techniques, we prove that for any positive integer k, the equation has a radial solution that changes signs exactly k times. Furthermore, we demonstrate that the energy of such solutions is an increasing function of k. Owing to the inherent characteristics of these equations, the methods used herein significantly differ from those used in the existing literature. Particularly, we discover a unified method to obtain infinitely many radial sign-changing solutions with nodal properties for local and nonlocal problems. [ABSTRACT FROM AUTHOR]

In this paper, we are dedicated to study the existence and asymptotic behavior of infinitely many nodal solutions of gauged Schrödinger equation with an asymptotically quintic nonlinear term. Based on variational methods, we show, for any integer k ⩾ 1 , the existence of a radial nodal solution that changes sign exactly k times. Meanwhile, we prove that the energy of such solutions is an increasing function of k. Furthermore, we verify the asymptotic behavior of these solutions upon varying the parameter λ . In particular, some analytical techniques are applied, which allows us to overcome the difficulties resulting from the complicated competition between the nonlocal term and the asymptotically quintic nonlinearity. Our results enrich the previous ones in the literature involved asymptotically quintic case. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in the following Schrödinger equation - Δ u + λ V (x) u = (I α ∗ | u | p ) | u | p - 2 u + | u | 4 u in R 3 , where λ is a positive parameter, V ∈ C (R , R +) and α ∈ (0 , 3) , p ∈ (2 + α , 3 + α) . Under some reasonable conditions on potential function V, particularly V allows to have nonisolated zero, we first establish the existence of positive ground-state solution and the corresponding energy estimates based on Nehari manifold. Subsequently, with the help of quantitative deformation lemma and invariant sets of descending flow, we also obtain the existence of ground-state sign-changing solution by adopting constrained minimization arguments on the sign-changing Nehari manifold. In this process, a new existence result of zero, which can be regarded as a generalization of Miranda's theorem, plays an essential role. Besides, the asymptotic behavior of sign-changing solutions is also studied when λ tends to infinity. [ABSTRACT FROM AUTHOR]

In this paper, we look for solutions to the following Choquard-type equation - Δ u + (V + λ) u = (I α ∗ | u | p ) | u | p - 2 u + μ (I α ∗ | u | q ) | u | q - 2 u in R N , having a prescribed mass ∫ R N u 2 = a > 0 , where λ ∈ R will arise as a Lagrange multiplier, N ⩾ 3 , I α is the Riesz potential, α ∈ (0 , N) , p ∈ (α ¯ , 2 α ∗ ] , q ∈ (α ¯ , 2 α ∗) , α ¯ = (N + α + 2) / N is the mass critical exponent, 2 α ∗ = (N + α) / (N - 2) is the Hardy–Littlewood–Sobolev upper critical exponent and μ > 0 is a constant. Under suitable conditions on the potential V, the above Choquard-type equation admits a positive ground state normalized solution by comparison arguments, in particular, when p = 2 α ∗ , μ needs to be larger and the Hardy–Littlewood–Sobolev subcritical approximation method is used. At the end of this paper, a new result on the regularity of solutions and Pohozaev identity to a more general Choquard-type equation is established. [ABSTRACT FROM AUTHOR]

Microsatellite instability (MSI), a vital mutator phenotype caused by DNA mismatch repair deficiency, is frequently observed in several tumors. MSI is recognized as a critical molecular biomarker for diagnosis, prognosis, and therapeutic selection in several cancers. Identifying MSI status for current gold standard methods based on experimental analysis is laborious, time-consuming, and costly. Although several computational methods based on machine learning have been proposed to identify MSI status, we need to further understand which machine learning model would favor identification for MSI and which feature subset is strongly related to MSI. On this basis, more effective machine learning-based methods can be developed to improve the performance of MSI status identification. In this work, we present MSINGB, an NGBoost-based method for identifying MSI status from tumor somatic mutation annotation data. MSINGB first evaluates the prediction performance of 11 popular machine learning algorithms and 9 deep learning models to identify MSI. Among 20 models, NGBoost, a novel natural gradient boosting method, achieves the overall best performance. MSINGB then introduces two feature selection strategies to find the compact feature subset, which is strongly related to MSI, and employs the SHAP approach to interpreting how selected features impact the model prediction. MSINGB achieves a better prediction performance on both the tenfold cross-validation test and independent test compared with state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Promoters short DNA sequences play vital roles in initiating gene transcription. However, it remains a challenge to identify promoters using conventional experiment techniques in a high-throughput manner. To this end, several computational predictors based on machine learning models have been developed, while their performance is unsatisfactory. In this study, we proposed a novel two-layer predictor, called PredPromoter-MF(2L), based on multi-source feature fusion and ensemble learning. PredPromoter-MF(2L) was developed based on various deep features learned by a pre-trained deep learning network model and sequence-derived features. Feature selection based on XGBoost was applied to reduce fused features dimensions, and a cascade deep forest model was trained on the selected feature subset for promoter prediction. The results both fivefold cross-validation and independent test demonstrated that PredPromoter-MF(2L) outperformed state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In this paper, we study solutions with a prescribed L 2 mass of a transmission problem of Kirchhoff type, which is an interface problem for elliptic operators in bounded domains of R 3 and arises in some physical systems in different connected media. Because of the presence of transmission/interface conditions, we first deduce a modified Gagliardo–Nirenberg inequality applicable to the Kirchhoff-type transmission problem, based on which the L 2 critical exponent is defined. Subsequently, we prove the existence of normalized solutions no matter whether the nonlinearity is L 2 subcritical, critical, or supercritical. In particular, in the supercritical case, we use an eigenvalue of the transmission problem to characterize the conditions for the existence of solutions. [ABSTRACT FROM AUTHOR]

The existence, nonexistence and multiplicity of positive radially symmetric solutions to a class of Schrödinger-Poisson type systems with critical nonlocal term are studied with variational methods. The existence of both the ground state solution and mountain pass type solutions are proved. It is shown that the parameter ranges of existence and nonexistence of positive solutions for the critical nonlocal case are completely different from the ones for the subcritical nonlocal system. [ABSTRACT FROM AUTHOR]

Using variational method, the authors get an existence result for positive solutions of a superlinear elliptic boundary value problem without assuming the P.S. condition. To prove the results in this paper, the authors adopt the method of gradient flow and use a new class of truncation functions. [ABSTRACT FROM AUTHOR]

Despite significant progress, our understanding of how specific oncogenes transform cells is still limited and likely underestimates the complexity of downstream signalling events. To address this gap, we use mass spectrometry-based chemical proteomics to characterize the global impact of an oncogene on the expressed kinome, and then functionally annotate the regulated kinases. As an example, we identify 63 protein kinases exhibiting altered expression and/or phosphorylation in Src-transformed mammary epithelial cells. An integrated siRNA screen identifies nine kinases, including SGK1, as being essential for Src-induced transformation. Accordingly, we find that Src positively regulates SGK1 expression in triple negative breast cancer cells, which exhibit a prominent signalling network governed by Src family kinases. Furthermore, combined inhibition of Src and SGK1 reduces colony formation and xenograft growth more effectively than either treatment alone. Therefore, this approach not only provides mechanistic insights into oncogenic transformation but also aids the design of improved therapeutic strategies. The systemic understanding of oncogenic kinase signalling is still limited. Here, the authors combine chemical proteomics with functional screens to assess the impact of oncogenic Src on the expressed kinome and identify SGK1 as a critical mediator of Src-induced cell transformation. [ABSTRACT FROM AUTHOR]

A Kirchhoff-type fractional elliptic system with Hartree-type nonlinearity is proposed to provide a unified framework for well-known nonlinear Schrödinger equations, Kirchhoff equations and Schrödinger-Poisson systems. The existence of nontrivial nonnegative ground state solutions to the system is proved when the coefficient of the potential function is larger than a threshold value, and a precise estimate of the threshold value is given for a prototypical example. It is also shown that the ground state solution concentrates on the zero set of the potential function when the coefficient tends to infinity. [ABSTRACT FROM AUTHOR]